A House trade subcommittee yesterday approved a resolution giving the president authority to negotiate and implement an agreement to restrict Japanese car and truck imports. But it aslo tacked on a warning to the U.S. auto industry to invest prudently any benefits it gets from the law.

Rep. Charles A. Vanik (D-Ohio), chairman of the House Ways and Means trade subcommittee, predicted that the politically sensitive measure to aid Detroit would pass both houses during the final days of the lame-duck session.

The original resolution, modified yesterday to make sure the proposed presidential power didn't circumvent existing trade laws, was intended to send a warning to the Japanese to cut back sales here of their small, fuel-efficient cars.

The committee members yesterday insisted the U.S. auto industry and the United Auto Workers union should get a stern message as well: that they must use any benefits from the legislation in investments within the United States and pass up large wage increases and other costs.

The subcommittee voted to include language in its report specifying that Detroit invest here.

"We have no guarantees on how Ford [motor Co.] and the UAW will spend this protection money, this black mail to the consumer," said Rep. Bill Frenzel (R-Minn.), the only subcommittee member of the 17 members present during debate to vote against the resolution.

During a hearing Tuesday on the legislation, a Ford Motor Co. executive assured the committee that any profits from the legislation would be invested in plants here.

Ford and the UAW have pinned their hopes for import relief on Congress following the refusal of the International Trade Commission grant restrictions on foreign car sales, particularly those from Japan. The ITC ruled that imports were not the major cause of Detroit's economic and unemployment problems.

If authority to implement an agreement for import restrictions is approved by Congress, the automaker and union must count on President-elect Ronald Reagan to use it since the Carter Administration said Tuesday that it would not.

"After months of debate, delay and confusion, this action sends a clear signal to Japan that the U.S. isn't going to stand by and let unbridled imports disrupt our markets and displace American workers," Ford chairman Philip Caldwell volunteered in a statement.

"We are particularly gratified by the overwhelming nonpartisan nature of the vote and the strong support shown by other members of the Senate and House who testified in favor of the resolution."

The legislation sent to the full House Ways and Means committee yesterday would grant the president authority to negotiate during a three-year period an agreement lasting until Jan. 1, 1984, to limit automobile and truck imports.

But the ailing industry must first present its case before the ITC. The president, after consulting with the secretary of Commerce and the U.S. Trade Representative, then could find that the industry is seriously injured and negotiate and implement import relief.

In addition, the legislation would exempt the president from antitrust laws in implementing the agreement.

Late last night the full committee agreed to consider the legislation today. Vanik said he hopes the House will consider the bill on Monday.

The Senate, in which similar legislation was introduced last August by Sen. Donald Riegle (D-Mich.), "wanted us to act first," Vanik said.

Passage of the resolution "can be done" Vanik continued, "and I fore-see it being done in the closing days of the session."